Finally something super interesting!

# Statistical Modelling

A statistical model identifies of the distribution from which your data ${x_{1},x_{2},…,x_{n}}$ is drawn.

- MAB algorithms builds up statistical models for each arm

For example, if we look at a data sample, and see that it looks like it follows a Normal Distribution, our our statistical model is $Y_{i}∼N(μ,σ_{2})$, but with $μ,σ_{2}$ unknown.

Notes

- Attributes of the population that you are interested in are typically the parameters of your model
- Finding a model is an
**empirical**question, not theoretical

Once we can identify some sort of statistical model for our data, the goal is to estimate the parameters $θ(x_{1},x_{2},…,x_{n})$ of this statistical model. This process is called Estimation.